Parametrization of aproximate algebraic surfaces by lines
IdentifiersPermanent link (URI): http://hdl.handle.net/10017/49602
Pérez Díaz, S., Sendra, J. & Sendra, J.R. 2005, “Parametrization of approximate algebraic surfaces by lines”, Computer Aided Geometric Design, vol. 22, no. 2, pp. 147-181.
GAIA II (IST-2002-35512)
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2004 Elsevier
In this paper we present an algorithm for parametrizing approximate algebraic surfaces by lines. The algorithm is applicable to ²-irreducible algebraic surfaces of degree d having an ²–singularity of multiplicity d−1, and therefore it generalizes the existing approximate parametrization algorithms. In particular, given a tolerance ² > 0 and an ²-irreducible algebraic surface V of degree d, the algorithm computes a new algebraic surface V , that is rational, as well as a rational parametrization of V . In addition, in the error analysis we show that the output surface V and the input surface V are close. More precisely, we prove that V lies in the offset region of V at distance, at most, O(² 1 2d ).
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